Continuous nonequilibrium transition driven by heat flow

Abstract

We discovered an out-of-equilibrium transition in the ideal gas between two walls, divided by an inner, adiabatic, movable wall. The system is driven out-of-equilibrium by supplying energy directly into the volume of the gas. At critical heat flux, we have found a continuous transition to the state with a low-density, hot gas on one side of the movable wall and a dense, cold gas on the other side. Molecular dynamic simulations of the soft-sphere fluid confirm the existence of the transition in the interacting system. We introduce a stationary state Helmholtz-like function whose minimum determines the stable positions of the internal wall. This transition can be used as a paradigm of transitions in stationary states and the Helmholtz-like function as a paradigm of the thermodynamic description of these states.

Thermodynamics of stationary states of the ideal gas in a heat flow

“…The reason for that is the fact that a particular form of the temperature profile does not play a role in the above calculations -the existence of the global steady state thermodynamics follows in the considered case from the fact that pressure is constant and it is a function of energy and volume, here p = 2U/3V . The ideal gas in the box volumetrically heated and separated by a movable wall considered by Zhang et al [17] also has these properties. Therefore, the steady state global thermodynamics formulated here also holds for Zhang et al [17] system, describing the continuous phase transition they consider.…”

“…The ideal gas in the box volumetrically heated and separated by a movable wall considered by Zhang et al [17] also has these properties. Therefore, the steady state global thermodynamics formulated here also holds for Zhang et al [17] system, describing the continuous phase transition they consider. We describe Zhang et al case in the next section.…”

“…The above expression is symmetric with respect to the interchange of T 1 and T 2 . Only S * contains information about heat absorbed/released in the system (see Eqs (9,17)) on top of the dissipative background (temperature profile). ∆S, on the other hand, controls the dissipative background since it depends on the entropy production given by [30]…”

“…( 14) does not vanish in stationary state, q (t) = 0. Zhang et al [17] consider ideal gas with uniform volumetric heating λ. In this case, in the energy balance ( 13) there appears the source term λ on the righthand side.…”

“…Zhang et al [17] considered an ideal gas between two parallel walls of area A located at z = −L and z = L. The system is translationally invariant in the x and y directions. The walls are kept at a fixed temperature T 0 and the energy is supplied into the system's volume in the form of heat with the flux J; the supplied energy per unit time and unit volume V = 2AL is λ = J/V .…”